Existence of meromorphic solutions of some generalized Fermat functional equations

The aim of this paper is twofold. Firstly, we study the non-existence of finite order meromorphic solutions to the Cubic type of Fermat functional equation \(f(z)^3-3\tau f(z)f(z+c)+f(z+c)^3=1\). In addition, the paper is concerned with the description of finite order entire solutions of the Quadratic type of Fermat functional equation \(f(z)^2-2\mu f(z)f(z+c)+f(z+c)^2=1\).